With verb "avoir", the past participle remains invariable, except if the direct object is placed BEFORE the verb (which is not the case here).
I see that key may be either "la clé" or "la clef". Is one of these terms used more frequently?
I see. "...the key of her car" of technically correct and a word-by-word translation but the English way of saying would usually be "the key TO her car", not "the key OF her car". A more relaxed expression would simply be "She lost her car key." Notice that there is not even a possessive form used "car's key"....but just "car key." And because people usually have several different keys (house or apartment key, car key, key to a cabinet or a lock), one might say "She lost her keys." But that's another story. Here it is specifically "la clé de sa voiture."
Yes, even 'the key for her car' would be more accepted I would think, than 'of her car'.
Why not "She lost the key to his car?" Would it change somehow if the key were not hers?
Thanks so much for your response! Just to clarify: with the "a lui" it would be ambiguous, or certainly "her"?
In this case "lui" is a stressed pronoun, exclusively masculine.
he lost the key to her car = il a perdu la clé de sa voiture à elle
Sorry, I meant without the lui. That is, in the original, it could be either he or she?
In the same sentence, "elle" followed by "sa" do point to the same person by default.